Question

what are the outliers for 0,5,6,7,8,13

Answer 1

Given:

The date set is:

0,5,6,7,8,13

To find:

The outliers for the given data set.

Solution:

We have,

0,5,6,7,8,13

Divide the data in two equal parts.

(0,5,6),(7,8,13)

Divide each parenthesis in two equal parts.

(0),5,(6),(7),8,(13)

Here, first quartile is $Q_1=5$ and the third quartile is $Q_3=8$.

The interquartile range (IQR) is:

$IQR=Q_3-Q_1$

$IQR=8-5$

$IQR=3$

The data lie outside the range $[Q_1-1.5IQR,Q_3+1.5IQR]$ is called outliers.

$[Q_1-1.5IQR,Q_3+1.5IQR]=[5-1.5(3),8+1.5(3)]$

$[Q_1-1.5IQR,Q_3+1.5IQR]=[5-4.5,8+4.5]$

$[Q_1-1.5IQR,Q_3+1.5IQR]=[0.5,12.5]$

The data values 0 and 13 lie outside the range [0.5,12.5].

Therefore, 0 and 13 are outliers of the given data set.